A man running on horizontal road finds the rain falling at angle - with the vertical- If he doubles his speed angle becomes - - With what angle with vertical whill rain appear to fall- when he triples his speed- The rain falls vertically down when he is at rest-

The correct option is C tan^ 1(2 tanβ tanα)Let the initial speed of the man be V. nbsp; V_MO = V î Let V_RO = xĵ (constant) tanα = V_MOV_RO = Vx when he ...

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Standard XII

Physics

Relative Motion: Rain Example

A man running...

Question

A man running on horizontal road finds the rain falling at angle $α$ with the vertical. If he doubles his speed angle becomes $β .$ With what angle with vertical whill rain appear to fall, when he triples his speed? The rain falls vertically down when he is at rest.

{tan}^{- 1} (2 tan α - tan β)

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{tan}^{- 1} (2 tan β + tan α)

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{tan}^{- 1} (2 tan α + tan β)

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{tan}^{- 1} (2 tan β - tan α)

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Solution

The correct option is D ${tan}^{- 1} (2 tan β - tan α)$
Let the initial speed of the man be V.
$_{M O} = V^i$
Let $_{R O} = - x^j (c o n s t a n t)$
$tan α = \frac{V_{M O}}{V_{R O}} = \frac{V}{x}$
when he doubles his speed.
$tan β = \frac{2 V}{x}$
when he triples his speed,
$tan γ = \frac{3 V}{x}$
$2 tan β - tan α = \frac{4 V}{x} - \frac{V}{x} = \frac{3 V}{x}$
$\Rightarrow 2 tan β - tan α = tan γ$
$\Rightarrow γ = {tan}^{- 1} (2 tan β - tan α)$

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A man running on horizontal road finds the rain falling at angle α with the vertical. If he doubles his speed angle becomes β. With what angle with vertical whill rain appear to fall, when he triples his speed? The rain falls vertically down when he is at rest.

A man running on horizontal road finds the rain falling at angle $α$ with the vertical. If he doubles his speed angle becomes $β .$ With what angle with vertical whill rain appear to fall, when he triples his speed? The rain falls vertically down when he is at rest.